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int x * (arctg x)^2 dx
Заранее спасибо!

int x * (arctg x)^2 dx = int arctg^2 x d(1/2 * x^2) = 1/2 * int (arctg x)^2 d(x^2) =
= 1/2 * x^2 * (arctg x)^2 - 1/2 * int x^2 d((arctg x)^2) =
= 1/2 * x^2 * (arctg x)^2 - 1/2 * int x^2 * 2 * arctg x * 1/(1 + x^2) dx =
= 1/2 * x^2 * (arctg x)^2 - int x^2/(x^2 + 1) * arctg x dx =
= 1/2 * x^2 * (arctg x)^2 - int (x^2 + 1 - 1)/(x^2 + 1) * arctg x dx =
= 1/2 * x^2 * (arctg x)^2 - int arctg x dx + int arctg x/(x^2 + 1) dx =
= 1/2 * x^2 * (arctg x)^2 - x * arctg x + int x d(arctg x) + int arctg x d(arctg x) =
= | t = arctg x | =
= 1/2 * x^2 * (arctg x)^2 - x * arctg x + int x/(1 + x^2) dx + int t dt =
= 1/2 * x^2 * (arctg x)^2 - x * arctg x + int 1/(1 + x^2) d(1/2 * x^2) + 1/2 * t^2 =
= | t = arctg x | =
= 1/2 * x^2 * (arctg x)^2 - x * arctg x + 1/2 * int 1/(1 + x^2) d(x^2) +
+ 1/2 * (arctg x)^2 = | x^2 = u | =
= 1/2 * x^2 * (arctg x)^2 - x * arctg x + 1/2 * int 1/(1 + u) du + 1/2 * (arctg x)^2 =
= 1/2 * x^2 * (arctg x)^2 - x * arctg x + 1/2 * ln |1 + u| + 1/2 * (arctg x)^2 + C =
= | u = x^2 | =
= 1/2 * x^2 * (arctg x)^2 - x * arctg x + 1/2 * ln (1 + x^2) + 1/2 * (arctg x)^2 + C =
= 1/2 * (x^2 + 1) * (arctg x)^2 - x * arctg x + 1/2 * ln (1 + x^2) + C

Cпасибо огромное)